Why the center of black holes should be different from neutron stars?

[Leonardo Muzzi]

Physically speaking, why the insides of the least massive black hole should be any different from the heaviest possible neutron star?

 

[russ_watters]

Physically speaking, why the insides of the least massive black hole should be any different from the heaviest possible neutron star?

Neutrons aren't strong enough to support themselves against the pressure.
https://en.m.wikipedia.org/wiki/Tolman–Oppenheimer–Volkoff_limit

 

[Leonardo Muzzi]

But that is also true for the center of a Neutron start, correct?

Let me elaborate a bit more: let's say we have a neutron start slowly gathering more matter (from any source) over time. At a certain point, this start will become a black hole, that is, an event horizon will form.

At this point, why would the contents of that black hole be any different from the neutron star that was there right before the event horizon formation?

 

[Nugatory]

But that is also true for the center of a Neutron start, correct?

No.

At this point, why would the contents of that black hole be any different from the neutron star that was there right before the event horizon formation?

A neutron star forms when the inwards pressure from the collapse is not sufficient to overcome the neutron degeneracy pressure, so the collapse stops and we have a core of neutrons. If the collapsing star is more massive the pressure from the collapse will be greater, and if large enough will overcome the neutron degeneracy pressure; the collapse will continue unchecked and instead of getting a core of neutrons we’ll get a black hole singularity.

 

[Leonardo Muzzi]

No.

A neutron star forms when the inwards pressure from the collapse is not sufficient to overcome the neutron degeneracy pressure, so the collapse stops and we have a core of neutrons. If the collapsing star is more massive the pressure from the collapse will be greater, and if large enough will overcome the neutron degeneracy pressure; the collapse will continue unchecked and instead of getting a core of neutrons we’ll get a black hole singularity.

If neutron degeneracy is not overcomed, black holes can't form?

 

[Nugatory]

If neutron degeneracy is not overcomed, black holes can't form?

Right

 

[PAllen]

Most of this discussion is about stellar collapse, and @Nugatory is correct in this context. However, for the general case of black holes in General Relativity, the equation of state doesn't matter when mass is large enough. The classic example is that if you had a dust cloud with the local density of air everywhere, but its size^* is that of the Milky Way, it would already be well inside its Schwarzschild Radius. It would have already lost any future causal connection to the rest of the universe, and its evolution to a singularity would already be as 'forced' as the arrival of tomorrow.

*There are subtleties in defining size, because we don't have Euclidean geometry. However, we can pick any nearly hypersurface orthogonal slice to define size, and the conclusion remains.

 

[russ_watters]

Most of this discussion is about stellar collapse, and @Nugatory is correct in this context. However, for the general case of black holes in General Relativity, the equation of state doesn't matter when mass is large enough. The classic example is that if you had a dust cloud with the local density of air everywhere, but its size^* is that of the Milky Way, it would already be well inside its Schwarzschild Radius.

But isn't that just a hypothetical mathematical model that has no connection to reality? E.G. such a dust cloud could neither form nor remain a cloud if it magically appeared.

 

[russ_watters]

At this point, why would the contents of that black hole be any different from the neutron star that was there right before the event horizon formation?

@Nugatory gave the scenario of a neutron star forming (or not) from a supernova. An additional scenario from the wiki link I gave is of two neutron stars merging. They didn't just form a bigger neutron star like two bubbles merging, but rather the combination was too massive for the neutrons to continue to support themselves and it is believed to have immediately collapsed into a black hole.

 

[PAllen]

But isn't that just a hypothetical mathematical model that has no connection to reality? E.G. such a dust cloud could neither form nor remain a cloud if it magically appeared.

The key point is that matter inside BH, for its short period of existence, need not have high density while still being inside the horizon. For example, if a planet entered a supermassive BH, it would be far into its (short) post horizon history before it experienced extreme tidal forces ripping it apart.

It is true that there is no plausible scenario for such gas cloud forming in a reasonable cosmology, but there are certainly initial conditions that don’t violate any laws or energy conditions that would have such cloud inside a horizon as a stage of their evolution. At a later stage, the cloud would be compressed in one direction, and stretched in another.

 

[Drakkith]

@Leonardo Muzzi Note that while we can confidently say that the material inside a black hole that's formed from the collapse of a neutron star must be very different than that of a neutron star, since the neutrons had to change into something else for the collapse to happen in the first place, we really have very little idea of what forms matter and energy might take inside a black hole, if any.

 

[alantheastronomer]

Physically speaking, why the insides of the least massive black hole should be any different from the heaviest possible neutron star?

That's a very thought-provoking question. The concept of a black hole came purely from theoretical considerations without regard for the real world, so your question shows real insight. If the neutron star were massive enough and it didn't collapse, you're right, it would form an event horizon external to it's surface and remain undisturbed, invisible to the outside world. The amount of mass it would take for this to happen is somewhere between five and ten solar masses, but alas, as @russ_watters pointed out, the mass limit for the most massive neutron stars is only two to three times the mass of the sun...

 

[PAllen]

That's a very thought-provoking question. The concept of a black hole came purely from theoretical considerations without regard for the real world, so your question shows real insight. If the neutron star were massive enough and it didn't collapse, you're right, it would form an event horizon external to it's surface and remain undisturbed, invisible to the outside world. The amount of mass it would take for this to happen is somewhere between five and ten solar masses, but alas, as @russ_watters pointed out, the mass limit for the most massive neutron stars is only two to three times the mass of the sun...

Well, you can conceptually posit a giant neutron inside it’s event horizon as a transitory state. But it would not remain undisturbed. At least per classical GR, it would rapidly be compressed and stretched, becoming a singular state very quickly, and as unavoidably as the arrival of tomorrow.

There are fantastically unlikely conditions to produce this. Consider 5 neutron stars moving perfectly to a common center. As they just begin merging, they would already be inside their event horizon (so an outside observer could get no information on the merger). However this state would be extremely transitory.

Of course, in the real world, this is kind of like an old joke about sharpshooters trying to make a cannonball by standing in a circle and firing towards its center on a signal, using lead bullets. The likely outcome would be less pleasant than the intended goal.

 

[Leonardo Muzzi]

Thanks all for the answers, appreciate.

Ok so from what I could understand, it is very well possible that the contents of a black hole are known objects, such as "5 neutron stars moving perfectly in a common center", or a "dust cloud the size of the milky way", although these scenarios will be temporary until these situations collapse. Therefore, there is no strict connection between the formation of a black hole and its contents, at least for a period.

Another conclusion is: whatever formed the black hole, even if a known object like the ones above, eventually will collapse. The result is not known because we don't know what happens with matter when it is put under such gravitational pressure: it is known that it won't be the same as a neutron star, as neutrons can't hold themselver against such pressure.

Are those correct?

 

[PAllen]

Thanks all for the answers, appreciate.

Ok so from what I could understand, it is very well possible that the contents of a black hole are known objects, such as "5 neutron stars moving perfectly in a common center", or a "dust cloud the size of the milky way", although these scenarios will be temporary until these situations collapse. Therefore, there is no strict connection between the formation of a black hole and its contents, at least for a period.

Another conclusion is: whatever formed the black hole, even if a known object like the ones above, eventually will collapse. The result is not known because we don't know what happens with matter when it is put under such gravitational pressure: it is known that it won't be the same as a neutron star, as neutrons can't hold themselver against such pressure.

Are those correct?

That is all correct, with a few caveats:

1) The possibilities mentioned in your first paragraph are possible "in principle" in the same sense as, after a 'break' of the initial triangle on a pool table, having a bunch of people hit all the balls such that the triangle is reformed and cue ejected from it. I gave a more realistic case of a ordinary matter existing within an event horizon as a planet crossing the horizon of a quiescent supermassive BH. This does not require ridiculously improbable initial conditions unlike the other cases I brought up.

2) "eventually will collapse" should better be phrased as "will collapse exceedingly fast".

 

[Leonardo Muzzi]

That is all correct, with a few caveats:

1) The possibilities mentioned in your first paragraph are possible "in principle" in the same sense as, after a 'break' of the initial triangle on a pool table, having a bunch of people hit all the balls such that the triangle is reformed and cue ejected from it. I gave a more realistic case of a ordinary matter existing within an event horizon as a planet crossing the horizon of a quiescent supermassive BH. This does not require ridiculously improbable initial conditions unlike the other cases I brought up.

2) "eventually will collapse" should better be phrased as "will collapse exceedingly fast".

Understood. Thanks.

Ok so exploring this a bit more, taking the scenario where a planet, or a neutron star, enters a black hole... for that brief period before the star's matter gets into the singularity, would this black hole have any characteristics visible outside the event horizon that are any different from another black hole with the same mass, rotation, and angular momentum?

For example, let's say there are detectors all around the black hole that can measure the pull of gravity or the spacetime curvature. For that moment when the start crosses the event horizon, and before it reaches the singularity, would these sensors capture different measures on the side where the star has just crossed the black hole? Even better, would the even horizon itself distorts a bit, given the higher concentration of matter on one side?

 

[PAllen]

Understood. Thanks.

Ok so exploring this a bit more, taking the scenario where a planet, or a neutron star, enters a black hole... for that brief period before the star's matter gets into the singularity, would this black hole have any characteristics visible outside the event horizon that are any different from another black hole with the same mass, rotation, and angular momentum?

For example, let's say there are detectors all around the black hole that can measure the pull of gravity or the spacetime curvature. For that moment when the start crosses the event horizon, and before it reaches the singularity, would these sensors capture different measures on the side where the star has just crossed the black hole? Even better, would the even horizon itself distorts a bit, given the higher concentration of matter on one side?

Good questions!

There is a theorem: a black hole has no hair. The meaning is that a any black hole settles quickly to a state characterized only by mass, charge, and angular momentum. However, a key word here is settling.

So, a planet falling into a supermassive BH would involve the horizon changing shape as the planet approached, and engulfing it as a bump on the prior horizon shape. Then, there would be what is called “ring down” as the horizon oscillates as it settles to a slightly larger spherical shape. The only way this would be detected from further away would be as gravitational waves. I believe, if you had precise detectors around the BH, that the distribution of gravitational waves would be a anisotropic, especially at first. The anisotropy would be your clue as to where the planet was captured.

 

[PAllen]

Per my last post, let me clarify that the detected gravitational waves are generated outside the horizon as the exterior spacetime settles to spherical symmetry. There are also complex dynamics at and inside the horizon, but these are not detectable outside.

 

[Leonardo Muzzi]

Good questions!

There is a theorem: a black hole has no hair. The meaning is that a any black hole settles quickly to a state characterized only by mass, charge, and angular momentum. However, a key word here is settling.

So, a planet falling into a supermassive BH would involve the horizon changing shape as the planet approached, and engulfing it as a bump on the prior horizon shape. Then, there would be what is called “ring down” as the horizon oscillates as it settles to a slightly larger spherical shape. The only way this would be detected from further away would be as gravitational waves. I believe, if you had precise detectors around the BH, that the distribution of gravitational waves would be a anisotropic, especially at first. The anisotropy would be your clue as to where the planet was captured.

That's all very interesting! I'm interested in the part where you mention a "bump" on the prior horizon shape. Let's say we have the planet being captured in a very obtuse angle and goes around the center, inside the horizon, before getting to the singularity. Would this movement be visible from outside, using the same or similar mechanism you describe for infering where the planet was captured? I'm thinking like, if a bump is created where the planet is captured, would this bump also "move" with the movement of the planet, or would the anisotropy in the gravitational waves describe the movement of the mass inside, as it describes the point where the planet is captured?

 

[Leonardo Muzzi]

Good questions!

There is a theorem: a black hole has no hair. The meaning is that a any black hole settles quickly to a state characterized only by mass, charge, and angular momentum. However, a key word here is settling.

So, a planet falling into a supermassive BH would involve the horizon changing shape as the planet approached, and engulfing it as a bump on the prior horizon shape. Then, there would be what is called “ring down” as the horizon oscillates as it settles to a slightly larger spherical shape. The only way this would be detected from further away would be as gravitational waves. I believe, if you had precise detectors around the BH, that the distribution of gravitational waves would be a anisotropic, especially at first. The anisotropy would be your clue as to where the planet was captured.

Also another question if I may: why the horizon oscillates, instead of just increasing in size?

 

[PeterDonis]

Physically speaking, why the insides of the least massive black hole should be any different from the heaviest possible neutron star?

Because the inside of a black hole is vacuum. A black hole is nothing like any ordinary stable object, not even a neutron star.

let's say we have a neutron start slowly gathering more matter (from any source) over time. At a certain point, this start will become a black hole, that is, an event horizon will form.

No, that's not what will happen. An ordinary stable object like a neutron star cannot have a radius smaller than 9/8 of the Schwarzschild radius for its mass. (This result is known as Buchdahl's Theorem.) So there is a finite gap between "the most compact possible ordinary object" and a black hole. There is no way to continuously go from one to the other in a sequence of quasi-stationary states. There has to be a discontinuous collapse process in between.

 

[PeterDonis]

Because the inside of a black hole is vacuum.

Actually, the inside of a black hole is not even an ordinary region of space like you are used to. One of its boundaries, the singularity at $r = 0$, is not a place in space, it's a moment of time. The other boundary, the event horizon, is an outgoing lightlike surface, which is neither a place in space nor a moment of time.

So asking "what is inside the black hole" is asking a question that already embodies implicit assumptions that are violated inside a black hole.

 

[PAllen]

Actually, the inside of a black hole is not even an ordinary region of space like you are used to. One of its boundaries, the singularity at $r = 0$, is not a place in space, it's a moment of time. The other boundary, the event horizon, is an outgoing lightlike surface, which is neither a place in space nor a moment of time.

So asking "what is inside the black hole" is asking a question that already embodies implicit assumptions that are violated inside a black hole.

There is an everyday situation that encompasses these boundary types, but with altogether different geometry. Consider a flashbulb going off. Then all events inside the flash propagation sphere up to one hour from the flash, would be such a spacetime region. I think most people would be comfortable talking about the interior of this region.

 

[PAllen]

Because the inside of a black hole is vacuum. A black hole is nothing like any ordinary stable object, not even a neutron star.

But a BH formed from collapse would have a matter spacetime region
and a vacuum spacetime region inside the horizon.

It is also possible for a propelled test body to cross the horizon shortly after the collapsing surface has (or after the horizon has emerged from the collapsing body is more precise), and land on the collapsing surface before the surface reaches the singularity.

 

[PeterDonis]

a BH formed from collapse would have a matter spacetime region
and a vacuum spacetime region inside the horizon

Yes, this is true. The matter region is collapsing, so it is still nothing like an ordinary stable object. Also see below.

It is also possible for a propelled test body to cross the horizon shortly after the collapsing surface has (or after the horizon has emerged from the collapsing body is more precise), and land on the collapsing surface before the surface reaches the singularity.

Yes, but only "shortly" after. Once "shortly" has passed, it is impossible for any object that crosses the horizon to reach the matter region at all. So, except for that short time period, the interior of the hole is vacuum in a practical sense as far as anyone outside it is concerned.

 

[PAllen]

Yes, this is true. The matter region is collapsing, so it is still nothing like an ordinary stable object. Also see below.
Yes, but only "shortly" after. Once "shortly" has passed, it is impossible for any object that crosses the horizon to reach the matter region at all. So, except for that short time period, the interior of the hole is vacuum in a practical sense as far as anyone outside it is concerned.

I agree with these statements. I don’t think I implied differently.

 

[PeterDonis]

I agree with these statements. I don’t think I implied differently.

You didn't. I was just explaining, in the light of your statements, why I originally said the interior of a black hole was vacuum--because, while that statement is not exactly true, unless you are jumping into a black hole right after its formation (and have a powerful enough rocket to catch up with the infalling matter in the collapse), it is true in a practical sense as far as you are concerned.